OFFSET
1,4
LINKS
Eric Weisstein's World of Mathematics, Goldbach Partition
Wikipedia, Goldbach's conjecture
FORMULA
a(n) = Sum_{i=1..n-1} i * (n-i) * c(i) * c(2*n-i), where c is the prime characteristic (A010051).
EXAMPLE
a(4) = 3; 2*4 = 8 has one Goldbach partition into distinct parts (5,3). The area of the triangle is then (5 - 3)*3/2 = 3.
a(8) = 30; 2*8 = 16 has two Goldbach partitions into distinct parts, (13,3) and (11,5). The sum of the areas of the two triangles is (13 - 3)*3/2 + (11 - 5)*5/2 = 15 + 15 = 30.
MATHEMATICA
Table[Sum[i (n - i) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {i, n - 1}], {n, 60}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 13 2020
STATUS
approved